Question

The radius of the circle $r=3cos\theta +4sin\theta$ is

• A. $3$
• B. $4$
• C. $5/2$
• D. $5$

Answer 1

The correct option is C $5/2$

Put $\cos \theta =\frac{x}{r}$ & $\sin \theta =\frac{y}{r}$ in $r=3\cos \theta +4\sin \theta$
where, $r=\sqrt{x^2+y^2}$
$r=\frac{3x}{r}+\frac{4y}{r}$
$\Rightarrow r^2=3x+4y$
$\Rightarrow x^2+y^2-3x-4y=0$
Therefore, radius $=\sqrt{{\left(\frac{3}{2}\right)}^2+{\left(\frac{4}{2}\right)}^2-0}=5/2$